To further investigate the peak around the LAC, variance of ODMR contrast was measured by varying the angle \( \theta \)  of magnetic field (Fig.REF c). Two broad peaks appear around 750G and 1240G corresponding to LAC of the excited state and the ground state respectively. This can be understood by noting the spin mixing between different spin states increases with angle around LAC, which results in a reduction of the ODMR contrast (Fig.REF a). The larger the tilted angle is, the more spin state mixes and the contrast reduces (Fig.REF c,d). However, for magnetic field B alignes along c axis (\( \theta = 0^{\circ } \) ), one can still observe the reduction of the ODMR contrast as well as the PL counts around LAC (Fig.REF b,c). We attribute this to the residual spin mixing induced by an effective tilted magnetic field due to hyperfine interaction to the surrounding nuclear spins [1]}, [2]}.
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